Reduced order modeling of modular parameter dependent structures based on proper orthogonal decomposition and mesh tying

Abstract

A model order reduction technique in combination with mesh tying is used to efficiently simulate many different structures that are assembled from a set of substructures. The stiffness matrices of the substructures are computed separately and assembled into a global stiffness matrix with tied contact formulation. Reducing the degrees of freedom of each substructure with a projection‐based model order reduction technique further decreases the computational time. The mode matrices that project the system into the low‐dimensional subspace are computed for each module separately with proper orthogonal decomposition and the method of snapshots. For the development and optimization of new construction strategies for fiber‐reinforced concrete, many different combinations of the modules have to be tested. The mechanical behavior of these modules depends on a set of parameters. Here the parameters are the fiber directions for transversely isotropic material behavior and parameters that describe the shape of the module. The sensitivity of the model order reduction technique to parameter changes requires a mode adaption technique to obtain reasonable results. Mode matrices for any parameters are computed by interpolating in a tangent space to the Grassmann manifold.